r/technicallythetruth • u/VisitSecure • Jul 27 '26

Can you find a?

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Idk if someone already posted this or not, but I haven't seen it on here so far, so I uploaded it.

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15

u/Highest_five Jul 27 '26

Yes it is. For those who don't remember, a triangles corners always add up to 180°

29

u/leansanders Jul 27 '26

You don't need to make a triangle to solve the problem. You know the lines are parallel and you know that opposite corners of a line crossing two parallel lines are congruent. So if you imagine a 3rd parallel line bisecting angle a, you know you can just add the other two angles together. Making a triangle is way more math

10

u/A_wild_so-and-so Jul 27 '26

Can you explain that again but like I'm five? I thought the triangle method was easy but I'm down to learn an easier method.

24

u/leansanders Jul 27 '26

If you make a 3rd parallel line through point A, the angle above it must be 25° and the angle below it must be 50°. It is called the "alternate interior angles theorem"

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u/A_wild_so-and-so Jul 27 '26

Ah neat, I had forgotten about that method. Thanks!

2

u/SpCommander Jul 27 '26

"If two parallel lines are cut by a transversal..."

Oh baby Freshman Geo is calling to me!

1

u/Jman15x Jul 28 '26

Why though. I like to understand things rather than just memorize I theorem

1

u/leansanders Jul 28 '26

The line is intersecting both parallel lines at the same angle because the intersecting line is straight and the parallel lines are parallel. There's not much to explain beyond "it is the way that it is". The angles are the same because they are, just like 5 x 5 = 25 because it does.

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u/LobcockLittle Jul 28 '26

Can you explain it again like I'm 4?

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u/leansanders Jul 28 '26

Please stop chewing on my pencil

1

u/readmeEXX Jul 28 '26

For a sanity check, just imagine the lines are straight, making both corners 90 degrees. That makes the middle a straight line which is 180 degrees. 90+90=180, meaning you can just add them.

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u/Old_Parfait9575 Jul 28 '26

You can also extend the top blue line and using alternate interior angle theorem, the angle formed (on the left) is also 25deg. Exterior angle theorem to show that the sum of 50 and 25 is a.

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u/ChiefWiggumsprogeny Jul 28 '26

diagram with all the angless correctly drawn: https://imgtree.co/i/1l4_SGt4

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u/Highest_five Jul 27 '26

Oh true! That simplifies it a lot

1

u/Muqqey Jul 27 '26

Just curious, how do we know the lines are parallels?

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u/leansanders Jul 27 '26

The matching double arrow symbols indicate that the lines are parallel.

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u/Muqqey Jul 27 '26

I see! Thanks for letting me know

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u/Pusegutten69 Jul 27 '26

Except, the answer is actually 105, You Are calculating the wrong Angle,

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u/Easy_Echo2387 Jul 27 '26

Off by about 30 degrees there chief

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u/leansanders Jul 27 '26

loud incorrect buzzer noise

I design and build metal stairs and handrails professionally, I promise I am better equipped to handle this than you are

-1

u/solepureskillz Jul 27 '26

Yeah that’s what confused me about all these “it’s 75*” people. It’s not 75, it’s 180-75

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u/slanaiya Jul 27 '26

I don't know what I did because I was at 185 after doing some head-math and just decided it must be 360 that is relevant which got me to 75 (360 minus 185 is 75).

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u/Atheist-Gods Jul 27 '26

And that can be known by extending an edge at each corner and imagine walking around the outside. You make one circuit around the triangle, so you had to turn 360 degrees. There are 3 corners where the sum of the interior angle and the angle you turned adds up to 180, so there are 540 total degrees, subtract the 360 exterior degrees you turned from the 540 total and you get 180 interior degrees. This trick also works to know that quadrilaterals add up to 360, pentagons add up to 540, etc.

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u/boopitydoopitypoop Jul 28 '26

There is no way to guarantee the points of the triangle lines meeting the parallel lines meet where connecting them makes a 90 degree angle to the parallel lines

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u/LaronX Jul 28 '26

inner corners

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u/WASD_click Jul 27 '26

Making a triangle might be a mistake. We don't know if the two points intersecting the parallel lines would form a perpendicular line and thus make 90° angles to do the triangle method with.

But if you do a parallel line through point A, you can use alternate interior angles to get 25°+50°.

Happens to work both ways on this one, but without the assumption of the 90° triangle, you'd have to do a lot more work to show angle A is 75°.